If a right triange has one leg length 4 inches and the hypotenuse length 8 inches, find the lenth of the other leg

Question

If a and b are the lengths of two legs of a right triangle and c is the length of the hypotenuse, then a^2+b^2=c^2. If a right triangle has one leg length 4 inches and the hypotenuse length 8 inches, find the length of the other leg

Answer 1

Given a=4 and c=8, what is b?

   a³ + b² = c²

   (4)² + b² = (8)²

     b² = 64-16

     b = √48

     b = 4√3

 

Now is a good time to introduce some "special triangles" that will appear in many, many math problems (and on tests).

   This one has sides of  n*1, n*2, and n*SQRT(3)       where n=4

   There is also              n*1, n*SQRT(2), and n*1       where n=1

   and more

Answer 2

a²+b²=c²    then c²-a²=b²

so 8²-4²=b² which leads to b = sqrt(64-16) = sqrt(48)  which simplifies to 4sqrt(3)